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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    <a name="line.17"></a>
<FONT color="green">018</FONT>    package org.apache.commons.math3.distribution;<a name="line.18"></a>
<FONT color="green">019</FONT>    <a name="line.19"></a>
<FONT color="green">020</FONT>    import java.io.Serializable;<a name="line.20"></a>
<FONT color="green">021</FONT>    import java.math.BigDecimal;<a name="line.21"></a>
<FONT color="green">022</FONT>    <a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.exception.MathArithmeticException;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.exception.NotStrictlyPositiveException;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.exception.NumberIsTooLargeException;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math3.exception.util.LocalizedFormats;<a name="line.26"></a>
<FONT color="green">027</FONT>    import org.apache.commons.math3.fraction.BigFraction;<a name="line.27"></a>
<FONT color="green">028</FONT>    import org.apache.commons.math3.fraction.BigFractionField;<a name="line.28"></a>
<FONT color="green">029</FONT>    import org.apache.commons.math3.fraction.FractionConversionException;<a name="line.29"></a>
<FONT color="green">030</FONT>    import org.apache.commons.math3.linear.Array2DRowFieldMatrix;<a name="line.30"></a>
<FONT color="green">031</FONT>    import org.apache.commons.math3.linear.Array2DRowRealMatrix;<a name="line.31"></a>
<FONT color="green">032</FONT>    import org.apache.commons.math3.linear.FieldMatrix;<a name="line.32"></a>
<FONT color="green">033</FONT>    import org.apache.commons.math3.linear.RealMatrix;<a name="line.33"></a>
<FONT color="green">034</FONT>    <a name="line.34"></a>
<FONT color="green">035</FONT>    /**<a name="line.35"></a>
<FONT color="green">036</FONT>     * Implementation of the Kolmogorov-Smirnov distribution.<a name="line.36"></a>
<FONT color="green">037</FONT>     *<a name="line.37"></a>
<FONT color="green">038</FONT>     * &lt;p&gt;<a name="line.38"></a>
<FONT color="green">039</FONT>     * Treats the distribution of the two-sided {@code P(D_n &lt; d)} where<a name="line.39"></a>
<FONT color="green">040</FONT>     * {@code D_n = sup_x |G(x) - G_n (x)|} for the theoretical cdf {@code G} and<a name="line.40"></a>
<FONT color="green">041</FONT>     * the empirical cdf {@code G_n}.<a name="line.41"></a>
<FONT color="green">042</FONT>     * &lt;/p&gt;<a name="line.42"></a>
<FONT color="green">043</FONT>     * &lt;p&gt;<a name="line.43"></a>
<FONT color="green">044</FONT>     * This implementation is based on [1] with certain quick decisions for extreme<a name="line.44"></a>
<FONT color="green">045</FONT>     * values given in [2].<a name="line.45"></a>
<FONT color="green">046</FONT>     * &lt;/p&gt;<a name="line.46"></a>
<FONT color="green">047</FONT>     * &lt;p&gt;<a name="line.47"></a>
<FONT color="green">048</FONT>     * In short, when wanting to evaluate {@code P(D_n &lt; d)}, the method in [1] is<a name="line.48"></a>
<FONT color="green">049</FONT>     * to write {@code d = (k - h) / n} for positive integer {@code k} and<a name="line.49"></a>
<FONT color="green">050</FONT>     * {@code 0 &lt;= h &lt; 1}. Then {@code P(D_n &lt; d) = (n! / n^n) * t_kk}, where<a name="line.50"></a>
<FONT color="green">051</FONT>     * {@code t_kk} is the {@code (k, k)}'th entry in the special matrix<a name="line.51"></a>
<FONT color="green">052</FONT>     * {@code H^n}, i.e. {@code H} to the {@code n}'th power.<a name="line.52"></a>
<FONT color="green">053</FONT>     * &lt;/p&gt;<a name="line.53"></a>
<FONT color="green">054</FONT>     * &lt;p&gt;<a name="line.54"></a>
<FONT color="green">055</FONT>     * References:<a name="line.55"></a>
<FONT color="green">056</FONT>     * &lt;ul&gt;<a name="line.56"></a>
<FONT color="green">057</FONT>     * &lt;li&gt;[1] &lt;a href="http://www.jstatsoft.org/v08/i18/"&gt;<a name="line.57"></a>
<FONT color="green">058</FONT>     * Evaluating Kolmogorov's Distribution&lt;/a&gt; by George Marsaglia, Wai<a name="line.58"></a>
<FONT color="green">059</FONT>     * Wan Tsang, and Jingbo Wang&lt;/li&gt;<a name="line.59"></a>
<FONT color="green">060</FONT>     * &lt;li&gt;[2] &lt;a href="http://www.jstatsoft.org/v39/i11/"&gt;<a name="line.60"></a>
<FONT color="green">061</FONT>     * Computing the Two-Sided Kolmogorov-Smirnov Distribution&lt;/a&gt; by Richard Simard<a name="line.61"></a>
<FONT color="green">062</FONT>     * and Pierre L'Ecuyer&lt;/li&gt;<a name="line.62"></a>
<FONT color="green">063</FONT>     * &lt;/ul&gt;<a name="line.63"></a>
<FONT color="green">064</FONT>     * Note that [1] contains an error in computing h, refer to<a name="line.64"></a>
<FONT color="green">065</FONT>     * &lt;a href="https://issues.apache.org/jira/browse/MATH-437"&gt;MATH-437&lt;/a&gt; for details.<a name="line.65"></a>
<FONT color="green">066</FONT>     * &lt;/p&gt;<a name="line.66"></a>
<FONT color="green">067</FONT>     *<a name="line.67"></a>
<FONT color="green">068</FONT>     * @see &lt;a href="http://en.wikipedia.org/wiki/Kolmogorov-Smirnov_test"&gt;<a name="line.68"></a>
<FONT color="green">069</FONT>     * Kolmogorov-Smirnov test (Wikipedia)&lt;/a&gt;<a name="line.69"></a>
<FONT color="green">070</FONT>     * @version $Id: KolmogorovSmirnovDistribution.java 1416643 2012-12-03 19:37:14Z tn $<a name="line.70"></a>
<FONT color="green">071</FONT>     */<a name="line.71"></a>
<FONT color="green">072</FONT>    public class KolmogorovSmirnovDistribution implements Serializable {<a name="line.72"></a>
<FONT color="green">073</FONT>    <a name="line.73"></a>
<FONT color="green">074</FONT>        /** Serializable version identifier. */<a name="line.74"></a>
<FONT color="green">075</FONT>        private static final long serialVersionUID = -4670676796862967187L;<a name="line.75"></a>
<FONT color="green">076</FONT>    <a name="line.76"></a>
<FONT color="green">077</FONT>        /** Number of observations. */<a name="line.77"></a>
<FONT color="green">078</FONT>        private int n;<a name="line.78"></a>
<FONT color="green">079</FONT>    <a name="line.79"></a>
<FONT color="green">080</FONT>        /**<a name="line.80"></a>
<FONT color="green">081</FONT>         * @param n Number of observations<a name="line.81"></a>
<FONT color="green">082</FONT>         * @throws NotStrictlyPositiveException if {@code n &lt;= 0}<a name="line.82"></a>
<FONT color="green">083</FONT>         */<a name="line.83"></a>
<FONT color="green">084</FONT>        public KolmogorovSmirnovDistribution(int n)<a name="line.84"></a>
<FONT color="green">085</FONT>            throws NotStrictlyPositiveException {<a name="line.85"></a>
<FONT color="green">086</FONT>            if (n &lt;= 0) {<a name="line.86"></a>
<FONT color="green">087</FONT>                throw new NotStrictlyPositiveException(LocalizedFormats.NOT_POSITIVE_NUMBER_OF_SAMPLES, n);<a name="line.87"></a>
<FONT color="green">088</FONT>            }<a name="line.88"></a>
<FONT color="green">089</FONT>    <a name="line.89"></a>
<FONT color="green">090</FONT>            this.n = n;<a name="line.90"></a>
<FONT color="green">091</FONT>        }<a name="line.91"></a>
<FONT color="green">092</FONT>    <a name="line.92"></a>
<FONT color="green">093</FONT>        /**<a name="line.93"></a>
<FONT color="green">094</FONT>         * Calculates {@code P(D_n &lt; d)} using method described in [1] with quick<a name="line.94"></a>
<FONT color="green">095</FONT>         * decisions for extreme values given in [2] (see above). The result is not<a name="line.95"></a>
<FONT color="green">096</FONT>         * exact as with<a name="line.96"></a>
<FONT color="green">097</FONT>         * {@link KolmogorovSmirnovDistribution#cdfExact(double)} because<a name="line.97"></a>
<FONT color="green">098</FONT>         * calculations are based on {@code double} rather than<a name="line.98"></a>
<FONT color="green">099</FONT>         * {@link org.apache.commons.math3.fraction.BigFraction}.<a name="line.99"></a>
<FONT color="green">100</FONT>         *<a name="line.100"></a>
<FONT color="green">101</FONT>         * @param d statistic<a name="line.101"></a>
<FONT color="green">102</FONT>         * @return the two-sided probability of {@code P(D_n &lt; d)}<a name="line.102"></a>
<FONT color="green">103</FONT>         * @throws MathArithmeticException if algorithm fails to convert {@code h}<a name="line.103"></a>
<FONT color="green">104</FONT>         * to a {@link org.apache.commons.math3.fraction.BigFraction} in expressing<a name="line.104"></a>
<FONT color="green">105</FONT>         * {@code d} as {@code (k - h) / m} for integer {@code k, m} and<a name="line.105"></a>
<FONT color="green">106</FONT>         * {@code 0 &lt;= h &lt; 1}.<a name="line.106"></a>
<FONT color="green">107</FONT>         */<a name="line.107"></a>
<FONT color="green">108</FONT>        public double cdf(double d) throws MathArithmeticException {<a name="line.108"></a>
<FONT color="green">109</FONT>            return this.cdf(d, false);<a name="line.109"></a>
<FONT color="green">110</FONT>        }<a name="line.110"></a>
<FONT color="green">111</FONT>    <a name="line.111"></a>
<FONT color="green">112</FONT>        /**<a name="line.112"></a>
<FONT color="green">113</FONT>         * Calculates {@code P(D_n &lt; d)} using method described in [1] with quick<a name="line.113"></a>
<FONT color="green">114</FONT>         * decisions for extreme values given in [2] (see above). The result is<a name="line.114"></a>
<FONT color="green">115</FONT>         * exact in the sense that BigFraction/BigReal is used everywhere at the<a name="line.115"></a>
<FONT color="green">116</FONT>         * expense of very slow execution time. Almost never choose this in real<a name="line.116"></a>
<FONT color="green">117</FONT>         * applications unless you are very sure; this is almost solely for<a name="line.117"></a>
<FONT color="green">118</FONT>         * verification purposes. Normally, you would choose<a name="line.118"></a>
<FONT color="green">119</FONT>         * {@link KolmogorovSmirnovDistribution#cdf(double)}<a name="line.119"></a>
<FONT color="green">120</FONT>         *<a name="line.120"></a>
<FONT color="green">121</FONT>         * @param d statistic<a name="line.121"></a>
<FONT color="green">122</FONT>         * @return the two-sided probability of {@code P(D_n &lt; d)}<a name="line.122"></a>
<FONT color="green">123</FONT>         * @throws MathArithmeticException if algorithm fails to convert {@code h}<a name="line.123"></a>
<FONT color="green">124</FONT>         * to a {@link org.apache.commons.math3.fraction.BigFraction} in expressing<a name="line.124"></a>
<FONT color="green">125</FONT>         * {@code d} as {@code (k - h) / m} for integer {@code k, m} and<a name="line.125"></a>
<FONT color="green">126</FONT>         * {@code 0 &lt;= h &lt; 1}.<a name="line.126"></a>
<FONT color="green">127</FONT>         */<a name="line.127"></a>
<FONT color="green">128</FONT>        public double cdfExact(double d) throws MathArithmeticException {<a name="line.128"></a>
<FONT color="green">129</FONT>            return this.cdf(d, true);<a name="line.129"></a>
<FONT color="green">130</FONT>        }<a name="line.130"></a>
<FONT color="green">131</FONT>    <a name="line.131"></a>
<FONT color="green">132</FONT>        /**<a name="line.132"></a>
<FONT color="green">133</FONT>         * Calculates {@code P(D_n &lt; d)} using method described in [1] with quick<a name="line.133"></a>
<FONT color="green">134</FONT>         * decisions for extreme values given in [2] (see above).<a name="line.134"></a>
<FONT color="green">135</FONT>         *<a name="line.135"></a>
<FONT color="green">136</FONT>         * @param d statistic<a name="line.136"></a>
<FONT color="green">137</FONT>         * @param exact whether the probability should be calculated exact using<a name="line.137"></a>
<FONT color="green">138</FONT>         * {@link org.apache.commons.math3.fraction.BigFraction} everywhere at the<a name="line.138"></a>
<FONT color="green">139</FONT>         * expense of very slow execution time, or if {@code double} should be used<a name="line.139"></a>
<FONT color="green">140</FONT>         * convenient places to gain speed. Almost never choose {@code true} in real<a name="line.140"></a>
<FONT color="green">141</FONT>         * applications unless you are very sure; {@code true} is almost solely for<a name="line.141"></a>
<FONT color="green">142</FONT>         * verification purposes.<a name="line.142"></a>
<FONT color="green">143</FONT>         * @return the two-sided probability of {@code P(D_n &lt; d)}<a name="line.143"></a>
<FONT color="green">144</FONT>         * @throws MathArithmeticException if algorithm fails to convert {@code h}<a name="line.144"></a>
<FONT color="green">145</FONT>         * to a {@link org.apache.commons.math3.fraction.BigFraction} in expressing<a name="line.145"></a>
<FONT color="green">146</FONT>         * {@code d} as {@code (k - h) / m} for integer {@code k, m} and<a name="line.146"></a>
<FONT color="green">147</FONT>         * {@code 0 &lt;= h &lt; 1}.<a name="line.147"></a>
<FONT color="green">148</FONT>         */<a name="line.148"></a>
<FONT color="green">149</FONT>        public double cdf(double d, boolean exact) throws MathArithmeticException {<a name="line.149"></a>
<FONT color="green">150</FONT>    <a name="line.150"></a>
<FONT color="green">151</FONT>            final double ninv = 1 / ((double) n);<a name="line.151"></a>
<FONT color="green">152</FONT>            final double ninvhalf = 0.5 * ninv;<a name="line.152"></a>
<FONT color="green">153</FONT>    <a name="line.153"></a>
<FONT color="green">154</FONT>            if (d &lt;= ninvhalf) {<a name="line.154"></a>
<FONT color="green">155</FONT>    <a name="line.155"></a>
<FONT color="green">156</FONT>                return 0;<a name="line.156"></a>
<FONT color="green">157</FONT>    <a name="line.157"></a>
<FONT color="green">158</FONT>            } else if (ninvhalf &lt; d &amp;&amp; d &lt;= ninv) {<a name="line.158"></a>
<FONT color="green">159</FONT>    <a name="line.159"></a>
<FONT color="green">160</FONT>                double res = 1;<a name="line.160"></a>
<FONT color="green">161</FONT>                double f = 2 * d - ninv;<a name="line.161"></a>
<FONT color="green">162</FONT>    <a name="line.162"></a>
<FONT color="green">163</FONT>                // n! f^n = n*f * (n-1)*f * ... * 1*x<a name="line.163"></a>
<FONT color="green">164</FONT>                for (int i = 1; i &lt;= n; ++i) {<a name="line.164"></a>
<FONT color="green">165</FONT>                    res *= i * f;<a name="line.165"></a>
<FONT color="green">166</FONT>                }<a name="line.166"></a>
<FONT color="green">167</FONT>    <a name="line.167"></a>
<FONT color="green">168</FONT>                return res;<a name="line.168"></a>
<FONT color="green">169</FONT>    <a name="line.169"></a>
<FONT color="green">170</FONT>            } else if (1 - ninv &lt;= d &amp;&amp; d &lt; 1) {<a name="line.170"></a>
<FONT color="green">171</FONT>    <a name="line.171"></a>
<FONT color="green">172</FONT>                return 1 - 2 * Math.pow(1 - d, n);<a name="line.172"></a>
<FONT color="green">173</FONT>    <a name="line.173"></a>
<FONT color="green">174</FONT>            } else if (1 &lt;= d) {<a name="line.174"></a>
<FONT color="green">175</FONT>    <a name="line.175"></a>
<FONT color="green">176</FONT>                return 1;<a name="line.176"></a>
<FONT color="green">177</FONT>            }<a name="line.177"></a>
<FONT color="green">178</FONT>    <a name="line.178"></a>
<FONT color="green">179</FONT>            return exact ? exactK(d) : roundedK(d);<a name="line.179"></a>
<FONT color="green">180</FONT>        }<a name="line.180"></a>
<FONT color="green">181</FONT>    <a name="line.181"></a>
<FONT color="green">182</FONT>        /**<a name="line.182"></a>
<FONT color="green">183</FONT>         * Calculates the exact value of {@code P(D_n &lt; d)} using method described<a name="line.183"></a>
<FONT color="green">184</FONT>         * in [1] and {@link org.apache.commons.math3.fraction.BigFraction} (see<a name="line.184"></a>
<FONT color="green">185</FONT>         * above).<a name="line.185"></a>
<FONT color="green">186</FONT>         *<a name="line.186"></a>
<FONT color="green">187</FONT>         * @param d statistic<a name="line.187"></a>
<FONT color="green">188</FONT>         * @return the two-sided probability of {@code P(D_n &lt; d)}<a name="line.188"></a>
<FONT color="green">189</FONT>         * @throws MathArithmeticException if algorithm fails to convert {@code h}<a name="line.189"></a>
<FONT color="green">190</FONT>         * to a {@link org.apache.commons.math3.fraction.BigFraction} in expressing<a name="line.190"></a>
<FONT color="green">191</FONT>         * {@code d} as {@code (k - h) / m} for integer {@code k, m} and<a name="line.191"></a>
<FONT color="green">192</FONT>         * {@code 0 &lt;= h &lt; 1}.<a name="line.192"></a>
<FONT color="green">193</FONT>         */<a name="line.193"></a>
<FONT color="green">194</FONT>        private double exactK(double d) throws MathArithmeticException {<a name="line.194"></a>
<FONT color="green">195</FONT>    <a name="line.195"></a>
<FONT color="green">196</FONT>            final int k = (int) Math.ceil(n * d);<a name="line.196"></a>
<FONT color="green">197</FONT>    <a name="line.197"></a>
<FONT color="green">198</FONT>            final FieldMatrix&lt;BigFraction&gt; H = this.createH(d);<a name="line.198"></a>
<FONT color="green">199</FONT>            final FieldMatrix&lt;BigFraction&gt; Hpower = H.power(n);<a name="line.199"></a>
<FONT color="green">200</FONT>    <a name="line.200"></a>
<FONT color="green">201</FONT>            BigFraction pFrac = Hpower.getEntry(k - 1, k - 1);<a name="line.201"></a>
<FONT color="green">202</FONT>    <a name="line.202"></a>
<FONT color="green">203</FONT>            for (int i = 1; i &lt;= n; ++i) {<a name="line.203"></a>
<FONT color="green">204</FONT>                pFrac = pFrac.multiply(i).divide(n);<a name="line.204"></a>
<FONT color="green">205</FONT>            }<a name="line.205"></a>
<FONT color="green">206</FONT>    <a name="line.206"></a>
<FONT color="green">207</FONT>            /*<a name="line.207"></a>
<FONT color="green">208</FONT>             * BigFraction.doubleValue converts numerator to double and the<a name="line.208"></a>
<FONT color="green">209</FONT>             * denominator to double and divides afterwards. That gives NaN quite<a name="line.209"></a>
<FONT color="green">210</FONT>             * easy. This does not (scale is the number of digits):<a name="line.210"></a>
<FONT color="green">211</FONT>             */<a name="line.211"></a>
<FONT color="green">212</FONT>            return pFrac.bigDecimalValue(20, BigDecimal.ROUND_HALF_UP).doubleValue();<a name="line.212"></a>
<FONT color="green">213</FONT>        }<a name="line.213"></a>
<FONT color="green">214</FONT>    <a name="line.214"></a>
<FONT color="green">215</FONT>        /**<a name="line.215"></a>
<FONT color="green">216</FONT>         * Calculates {@code P(D_n &lt; d)} using method described in [1] and doubles<a name="line.216"></a>
<FONT color="green">217</FONT>         * (see above).<a name="line.217"></a>
<FONT color="green">218</FONT>         *<a name="line.218"></a>
<FONT color="green">219</FONT>         * @param d statistic<a name="line.219"></a>
<FONT color="green">220</FONT>         * @return the two-sided probability of {@code P(D_n &lt; d)}<a name="line.220"></a>
<FONT color="green">221</FONT>         * @throws MathArithmeticException if algorithm fails to convert {@code h}<a name="line.221"></a>
<FONT color="green">222</FONT>         * to a {@link org.apache.commons.math3.fraction.BigFraction} in expressing<a name="line.222"></a>
<FONT color="green">223</FONT>         * {@code d} as {@code (k - h) / m} for integer {@code k, m} and<a name="line.223"></a>
<FONT color="green">224</FONT>         * {@code 0 &lt;= h &lt; 1}.<a name="line.224"></a>
<FONT color="green">225</FONT>         */<a name="line.225"></a>
<FONT color="green">226</FONT>        private double roundedK(double d) throws MathArithmeticException {<a name="line.226"></a>
<FONT color="green">227</FONT>    <a name="line.227"></a>
<FONT color="green">228</FONT>            final int k = (int) Math.ceil(n * d);<a name="line.228"></a>
<FONT color="green">229</FONT>            final FieldMatrix&lt;BigFraction&gt; HBigFraction = this.createH(d);<a name="line.229"></a>
<FONT color="green">230</FONT>            final int m = HBigFraction.getRowDimension();<a name="line.230"></a>
<FONT color="green">231</FONT>    <a name="line.231"></a>
<FONT color="green">232</FONT>            /*<a name="line.232"></a>
<FONT color="green">233</FONT>             * Here the rounding part comes into play: use<a name="line.233"></a>
<FONT color="green">234</FONT>             * RealMatrix instead of FieldMatrix&lt;BigFraction&gt;<a name="line.234"></a>
<FONT color="green">235</FONT>             */<a name="line.235"></a>
<FONT color="green">236</FONT>            final RealMatrix H = new Array2DRowRealMatrix(m, m);<a name="line.236"></a>
<FONT color="green">237</FONT>    <a name="line.237"></a>
<FONT color="green">238</FONT>            for (int i = 0; i &lt; m; ++i) {<a name="line.238"></a>
<FONT color="green">239</FONT>                for (int j = 0; j &lt; m; ++j) {<a name="line.239"></a>
<FONT color="green">240</FONT>                    H.setEntry(i, j, HBigFraction.getEntry(i, j).doubleValue());<a name="line.240"></a>
<FONT color="green">241</FONT>                }<a name="line.241"></a>
<FONT color="green">242</FONT>            }<a name="line.242"></a>
<FONT color="green">243</FONT>    <a name="line.243"></a>
<FONT color="green">244</FONT>            final RealMatrix Hpower = H.power(n);<a name="line.244"></a>
<FONT color="green">245</FONT>    <a name="line.245"></a>
<FONT color="green">246</FONT>            double pFrac = Hpower.getEntry(k - 1, k - 1);<a name="line.246"></a>
<FONT color="green">247</FONT>    <a name="line.247"></a>
<FONT color="green">248</FONT>            for (int i = 1; i &lt;= n; ++i) {<a name="line.248"></a>
<FONT color="green">249</FONT>                pFrac *= (double) i / (double) n;<a name="line.249"></a>
<FONT color="green">250</FONT>            }<a name="line.250"></a>
<FONT color="green">251</FONT>    <a name="line.251"></a>
<FONT color="green">252</FONT>            return pFrac;<a name="line.252"></a>
<FONT color="green">253</FONT>        }<a name="line.253"></a>
<FONT color="green">254</FONT>    <a name="line.254"></a>
<FONT color="green">255</FONT>        /***<a name="line.255"></a>
<FONT color="green">256</FONT>         * Creates {@code H} of size {@code m x m} as described in [1] (see above).<a name="line.256"></a>
<FONT color="green">257</FONT>         *<a name="line.257"></a>
<FONT color="green">258</FONT>         * @param d statistic<a name="line.258"></a>
<FONT color="green">259</FONT>         * @return H matrix<a name="line.259"></a>
<FONT color="green">260</FONT>         * @throws NumberIsTooLargeException if fractional part is greater than 1<a name="line.260"></a>
<FONT color="green">261</FONT>         * @throws FractionConversionException if algorithm fails to convert<a name="line.261"></a>
<FONT color="green">262</FONT>         * {@code h} to a {@link org.apache.commons.math3.fraction.BigFraction} in<a name="line.262"></a>
<FONT color="green">263</FONT>         * expressing {@code d} as {@code (k - h) / m} for integer {@code k, m} and<a name="line.263"></a>
<FONT color="green">264</FONT>         * {@code 0 &lt;= h &lt; 1}.<a name="line.264"></a>
<FONT color="green">265</FONT>         */<a name="line.265"></a>
<FONT color="green">266</FONT>        private FieldMatrix&lt;BigFraction&gt; createH(double d)<a name="line.266"></a>
<FONT color="green">267</FONT>                throws NumberIsTooLargeException, FractionConversionException {<a name="line.267"></a>
<FONT color="green">268</FONT>    <a name="line.268"></a>
<FONT color="green">269</FONT>            int k = (int) Math.ceil(n * d);<a name="line.269"></a>
<FONT color="green">270</FONT>    <a name="line.270"></a>
<FONT color="green">271</FONT>            int m = 2 * k - 1;<a name="line.271"></a>
<FONT color="green">272</FONT>            double hDouble = k - n * d;<a name="line.272"></a>
<FONT color="green">273</FONT>    <a name="line.273"></a>
<FONT color="green">274</FONT>            if (hDouble &gt;= 1) {<a name="line.274"></a>
<FONT color="green">275</FONT>                throw new NumberIsTooLargeException(hDouble, 1.0, false);<a name="line.275"></a>
<FONT color="green">276</FONT>            }<a name="line.276"></a>
<FONT color="green">277</FONT>    <a name="line.277"></a>
<FONT color="green">278</FONT>            BigFraction h = null;<a name="line.278"></a>
<FONT color="green">279</FONT>    <a name="line.279"></a>
<FONT color="green">280</FONT>            try {<a name="line.280"></a>
<FONT color="green">281</FONT>                h = new BigFraction(hDouble, 1.0e-20, 10000);<a name="line.281"></a>
<FONT color="green">282</FONT>            } catch (FractionConversionException e1) {<a name="line.282"></a>
<FONT color="green">283</FONT>                try {<a name="line.283"></a>
<FONT color="green">284</FONT>                    h = new BigFraction(hDouble, 1.0e-10, 10000);<a name="line.284"></a>
<FONT color="green">285</FONT>                } catch (FractionConversionException e2) {<a name="line.285"></a>
<FONT color="green">286</FONT>                    h = new BigFraction(hDouble, 1.0e-5, 10000);<a name="line.286"></a>
<FONT color="green">287</FONT>                }<a name="line.287"></a>
<FONT color="green">288</FONT>            }<a name="line.288"></a>
<FONT color="green">289</FONT>    <a name="line.289"></a>
<FONT color="green">290</FONT>            final BigFraction[][] Hdata = new BigFraction[m][m];<a name="line.290"></a>
<FONT color="green">291</FONT>    <a name="line.291"></a>
<FONT color="green">292</FONT>            /*<a name="line.292"></a>
<FONT color="green">293</FONT>             * Start by filling everything with either 0 or 1.<a name="line.293"></a>
<FONT color="green">294</FONT>             */<a name="line.294"></a>
<FONT color="green">295</FONT>            for (int i = 0; i &lt; m; ++i) {<a name="line.295"></a>
<FONT color="green">296</FONT>                for (int j = 0; j &lt; m; ++j) {<a name="line.296"></a>
<FONT color="green">297</FONT>                    if (i - j + 1 &lt; 0) {<a name="line.297"></a>
<FONT color="green">298</FONT>                        Hdata[i][j] = BigFraction.ZERO;<a name="line.298"></a>
<FONT color="green">299</FONT>                    } else {<a name="line.299"></a>
<FONT color="green">300</FONT>                        Hdata[i][j] = BigFraction.ONE;<a name="line.300"></a>
<FONT color="green">301</FONT>                    }<a name="line.301"></a>
<FONT color="green">302</FONT>                }<a name="line.302"></a>
<FONT color="green">303</FONT>            }<a name="line.303"></a>
<FONT color="green">304</FONT>    <a name="line.304"></a>
<FONT color="green">305</FONT>            /*<a name="line.305"></a>
<FONT color="green">306</FONT>             * Setting up power-array to avoid calculating the same value twice:<a name="line.306"></a>
<FONT color="green">307</FONT>             * hPowers[0] = h^1 ... hPowers[m-1] = h^m<a name="line.307"></a>
<FONT color="green">308</FONT>             */<a name="line.308"></a>
<FONT color="green">309</FONT>            final BigFraction[] hPowers = new BigFraction[m];<a name="line.309"></a>
<FONT color="green">310</FONT>            hPowers[0] = h;<a name="line.310"></a>
<FONT color="green">311</FONT>            for (int i = 1; i &lt; m; ++i) {<a name="line.311"></a>
<FONT color="green">312</FONT>                hPowers[i] = h.multiply(hPowers[i - 1]);<a name="line.312"></a>
<FONT color="green">313</FONT>            }<a name="line.313"></a>
<FONT color="green">314</FONT>    <a name="line.314"></a>
<FONT color="green">315</FONT>            /*<a name="line.315"></a>
<FONT color="green">316</FONT>             * First column and last row has special values (each other reversed).<a name="line.316"></a>
<FONT color="green">317</FONT>             */<a name="line.317"></a>
<FONT color="green">318</FONT>            for (int i = 0; i &lt; m; ++i) {<a name="line.318"></a>
<FONT color="green">319</FONT>                Hdata[i][0] = Hdata[i][0].subtract(hPowers[i]);<a name="line.319"></a>
<FONT color="green">320</FONT>                Hdata[m - 1][i] = Hdata[m - 1][i].subtract(hPowers[m - i - 1]);<a name="line.320"></a>
<FONT color="green">321</FONT>            }<a name="line.321"></a>
<FONT color="green">322</FONT>    <a name="line.322"></a>
<FONT color="green">323</FONT>            /*<a name="line.323"></a>
<FONT color="green">324</FONT>             * [1] states: "For 1/2 &lt; h &lt; 1 the bottom left element of the matrix<a name="line.324"></a>
<FONT color="green">325</FONT>             * should be (1 - 2*h^m + (2h - 1)^m )/m!" Since 0 &lt;= h &lt; 1, then if h &gt;<a name="line.325"></a>
<FONT color="green">326</FONT>             * 1/2 is sufficient to check:<a name="line.326"></a>
<FONT color="green">327</FONT>             */<a name="line.327"></a>
<FONT color="green">328</FONT>            if (h.compareTo(BigFraction.ONE_HALF) == 1) {<a name="line.328"></a>
<FONT color="green">329</FONT>                Hdata[m - 1][0] = Hdata[m - 1][0].add(h.multiply(2).subtract(1).pow(m));<a name="line.329"></a>
<FONT color="green">330</FONT>            }<a name="line.330"></a>
<FONT color="green">331</FONT>    <a name="line.331"></a>
<FONT color="green">332</FONT>            /*<a name="line.332"></a>
<FONT color="green">333</FONT>             * Aside from the first column and last row, the (i, j)-th element is<a name="line.333"></a>
<FONT color="green">334</FONT>             * 1/(i - j + 1)! if i - j + 1 &gt;= 0, else 0. 1's and 0's are already<a name="line.334"></a>
<FONT color="green">335</FONT>             * put, so only division with (i - j + 1)! is needed in the elements<a name="line.335"></a>
<FONT color="green">336</FONT>             * that have 1's. There is no need to calculate (i - j + 1)! and then<a name="line.336"></a>
<FONT color="green">337</FONT>             * divide - small steps avoid overflows.<a name="line.337"></a>
<FONT color="green">338</FONT>             *<a name="line.338"></a>
<FONT color="green">339</FONT>             * Note that i - j + 1 &gt; 0 &lt;=&gt; i + 1 &gt; j instead of j'ing all the way to<a name="line.339"></a>
<FONT color="green">340</FONT>             * m. Also note that it is started at g = 2 because dividing by 1 isn't<a name="line.340"></a>
<FONT color="green">341</FONT>             * really necessary.<a name="line.341"></a>
<FONT color="green">342</FONT>             */<a name="line.342"></a>
<FONT color="green">343</FONT>            for (int i = 0; i &lt; m; ++i) {<a name="line.343"></a>
<FONT color="green">344</FONT>                for (int j = 0; j &lt; i + 1; ++j) {<a name="line.344"></a>
<FONT color="green">345</FONT>                    if (i - j + 1 &gt; 0) {<a name="line.345"></a>
<FONT color="green">346</FONT>                        for (int g = 2; g &lt;= i - j + 1; ++g) {<a name="line.346"></a>
<FONT color="green">347</FONT>                            Hdata[i][j] = Hdata[i][j].divide(g);<a name="line.347"></a>
<FONT color="green">348</FONT>                        }<a name="line.348"></a>
<FONT color="green">349</FONT>                    }<a name="line.349"></a>
<FONT color="green">350</FONT>                }<a name="line.350"></a>
<FONT color="green">351</FONT>            }<a name="line.351"></a>
<FONT color="green">352</FONT>    <a name="line.352"></a>
<FONT color="green">353</FONT>            return new Array2DRowFieldMatrix&lt;BigFraction&gt;(BigFractionField.getInstance(), Hdata);<a name="line.353"></a>
<FONT color="green">354</FONT>        }<a name="line.354"></a>
<FONT color="green">355</FONT>    }<a name="line.355"></a>




























































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